Corpus ID: 235436247

The local period integrals and essential vectors

  title={The local period integrals and essential vectors},
  author={Yeongseong Jo},
By applying the formula for essential Whittaker functions established by Matringe and Miyauchi, we study five integral representations for irreducible admissible generic representations of GLn over p-adic fields. In each case, we show that the integrals achieve local formal L-functions defined by Langlands parameters, when the test vector is associated to the new form. We give the relation between local periods involving essential Whittaker functions and special values of formal L-factors at s… Expand


Let F be a non-archimedean local field of characteristic zero. Jacquet and Shalika attached a family of zeta integrals to unitary irreducible generic representations π of GLn(F). In this paper, weExpand
On the residue method for period integrals
By applying the residue method for period integrals and Langlands-Shahidi's theory for residues of Eisenstein series, we study the period integrals for six spherical varieties. For each sphericalExpand
Extension of Whittaker functions and test vectors
We show that certain products of Whittaker functions and Schwartz functions on a general linear group extend to Whittaker functions on a larger general linear group. This generalizes results ofExpand
Distinguished representations and exceptional poles of the Asai-L-function
Let K/F be a quadratic extension of p-adic fields. We show that a generic irreducible representation of GL(n, K) is distinguished if and only if its Rankin-Selberg Asai L-function has an exceptionalExpand
On representations distinguished by unitary groups
Let E/F be a quadratic extension of number fields. We study periods and regularized periods of cusp forms and Eisenstein series on $\operatorname {GL}_{n}( \mathbf {A}_{E})$ over a unitary group of aExpand
On epsilon factors attached to supercuspidal representations of unramified U(2,1)
Let G be the unramified unitary group in three variables defined over a p-adic field F of odd resudual characteristic. Gelbart, Piatetski-Shapiro and Baruch attached zeta integrals of Rankin-SelbergExpand
Whittaker functions associated to newforms for GL(n) over p-adic fields
Let F be a non-archimedean local field of characteristic zero. Jacquet, Piatetski-Shapiro and Shalika introduced the notion of newforms for irreducible generic representations of GL_n(F). In thisExpand
The characterization of theta-distinguished representations of GL(n)
Let θ and θ’ be a pair of exceptional representations in the sense of Kazhdan and Patterson [KP84], of a metaplectic double cover of GLn. The tensor θ ⊗ θ’ is a (very large) representation of GLn. WeExpand
Gamma Factors, Root Numbers, and Distinction
Abstract We study a relation between distinction and special values of local invariants for representations of the general linear group over a quadratic extension of $p$ -adic fields. We show thatExpand
Test vectors for Rankin–Selberg L-functions
We study the local zeta integrals attached to a pair of generic representations $(\pi,\tau)$ of $GL_n\times GL_m$, $n>m$, over a $p$-adic field. Through a process of unipotent averaging we produce aExpand